2024-02-03
Hypothesis testing is a statistical method used to make inferences about population parameters based on a sample of data.
It also involves setting up a hypothesis, after which we collecting data, and then using the data and assessing the evidence we either accept or reject the hypothesis.
In hypothesis testing, the critical range represents the range of values within which we would fail to reject the null hypothesis. It is determined by the confidence level.
The formula for the one-sample z-test is given by:
\[ Z = \frac{{\bar{X} - \mu}}{{\frac{\sigma}{\sqrt{n}}}} \]
The formula for the two-sample t-test is:
\[ t = \frac{{\bar{X}_1 - \bar{X}_2}}{{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}} \]
The chi-square test statistic is calculated as:
\[ \chi^2 = \sum \frac{{(O_i - E_i)^2}}{{E_i}} \]